a comparision study of time domain equalization technique using ultrawide band receivers performance...

8/9/2019 A COMPARISION STUDY OF TIME DOMAIN EQUALIZATION TECHNIQUE USING ULTRAWIDE BAND RECEIVERS PERFORM

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International Journal of Computer Networks & Communications (IJCNC), Vol.2, No.4, July 2010

DOI : 10.5121/ijcnc.2010.2403 22

ACOMPARISIONSTUDYOFTIMEDOMAIN

EQUALIZATIONTECHNIQUEUSING

ULTRAWIDEBANDRECEIVERS

PERFORMANCEFORHIGHDATARATEWPANSYSTEM

Susmita Das, Member, IEEE*

and Bikramaditya Das*

*Department of Electrical Engineering, National Institute of Technology,

Rourkela -769008, [email protected]

[email protected]

ABSTRACT

For high data rate ultra wideband communication system, performance comparison of Rake, MMSE and

Rake-MMSE receivers is attempted in this paper. We have taken into account of impact of all the

parameters such as the effect of the number of Rake fingers and equalizer taps on the error performance

by combating ISI are the major focus of our research. The bit error rate performances are investigated

using semi analytical approach and Monte-Carlo simulation on IEEE 802.15.3a UWB channel models. A

detail study on UWB channel model (IEEE 802.15.3a) is carried out using four channel models CM1-

CM4. Simulation results show that the bit error rate probability of rake-mmse receiver is much better

than Rake receiver and MMSE equalizer. Within the distance 0 to 4 meter Rake-MMSE performs better in

CM1 (LOS) channel model than that of CM2 (NLOS) channel model. Further the simulation results on

non-line of sight indoor channel models illustrate bit error rate performance of Rake-MMSE improves for

CM3 model with smaller spread compared to CM4 channel model. We show that for a MMSE equalizer

operating at low to medium SNRs, the number of Rake fingers is the dominant factor to improve system

performance, while at high SNRs the number of equalizer taps plays a more significant role in reducingerror rates.

KEYWORDS

UWB, Rake receiver, MMSE, Rake-MMSE, Bit Error Rate.

1.INTRODUCTION

Ultra Wideband Radio (UWB) is an emerging technology with big promise in imaging systems,

vehicular radar systems, and communication and measurement systems. UWB technology hasfor many years been used in radar and military communications but has not been allowed on the

open market prior to 2002. In April 2002, the federal communication commission (FCC) lifted

the restriction on the use of UWB technology for non-military applications. Since then, moreindustries have started developing UWB systems. UWB systems send information with

extremely short duration pulses, therefore allowing high speed data communication and

diversity against multipath. Several attempts are being made to use UWB at the physical layerfor personal area networks (PAN) to meet the FCC standards. FCC has released 3.1 GHz to 10.6

GHz frequency spectrum with a restriction on minimum transmission bandwidth of 500 MHz.In order to reduce interference with existing narrowband communication systems the maximum

transmit power spectral density of UWB is restricted to -41.3 dBm/MHz, which restricts the useof UWB to PAN. Ultra-wideband (UWB) has recently evoked great interest and its potential


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strength lies in its use of extremely wide transmission bandwidth. Furthermore, UWB isemerging as a solution for the IEEE 802.15a (TG3a) standard which is to provide a low

complexity, low cost, low power consumption and high data-rate among Wireless Personal AreaNetwork (WPAN) devices. An aspect of UWB transmission is to combat multipath propagationeffects. Rake receivers can be employed since they are able to provide multipath diversity [1-3].

Another aspect is to eliminate or combat the inter-symbol interference (ISI) which distorts the

transmitted signal and causes bit errors at the receiver, especially when the transmission data

rate is very high as well as for which are not well synchronized. In [1,3,4], the rakedecorrelating effect was mentioned as a way to combat ISI. Combination of spatial diversity

combining and equalization is a well established scheme for frequency selective fading channels[10]. In [5], a combined rake and equalizer structure was proposed for high data rate UWB

systems. In this paper, the performance of a rake-MMSE-equalizer receiver similar to [5] is

investigated for different number of rake fingers and equalizer taps using a semi-analyticalapproach. We propose at first to study time equalization with combined Rake-mmse equalizerstructure. We show that, for a MMSE equalizer [6] operating at low to medium SNRs, the

number of Rake fingers is the dominant factor to improve system performance, while, at highSNRs the number of equalizer taps plays a more significant role in reducing error rates[7-8].

The rest of the paper is organized as follows. In Section 2 we study the signals and systemmodel for IEEE UWB channel modelling. Section 3 is devoted principles of equalizations andreceiver structure. In section 4 we study performance analysis for Rake-MMSE receiver.

Simulation results are discussed in Section 5. Section 6 concludes the paper.

2.SIGNALSANDSYSTEMMODEL

For a single user system, the continuous transmitted data stream is written

+

=

=k

sTktpkdtA ).().()( (1)

Whered(k)are stationary uncorrelated BPSK data and Ts is the symbol duration. Throughoutthis paper we consider the application of a root raised cosine (RRC) transmit filterp(t) with roll-

off factor = 0.3. The UWB pulsep(t) has duration Tuwb (Tuwb < Ts ).

The channel models used in this paper are the model proposed by IEEE 802.15.3a Study Group

[10]. In the normalized models provided by IEEE 802.15.3a Study Group, different channelcharacteristics are put together under four channel model scenarios having rms delay spreads

ranging from 5 to 26 nsec. For this paper four channel models, derived from the IEEE 802.15channel modelling working group. In IEEE 802.15.3a working group, the UWB channel is

further classified into four models. Channel model 1 (CM1) represents LOS and distance from 0to 4 m UWB channel, while channel model 2 (CM2) represents NLOS and distance from 0 to 4

m UWB channel. Distance from 4 m to 10 m and NLOS UWB channel is modelled as CM3 and

distance over 10 m NLOS UWB channels are all classified into the extreme model CM4.

The impulse response can be written as

=

=M

p

pp thth0

)(.)( (2)

ParameterMis the total number of paths in the channel.


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3.PRINCIPLEOF RECEIVERSSTRUCTURE

3.1. RAKE RECEIVER

Rake receivers are used in time-hopping impulse radio systems and direct sequence spread

spectrum systems (DS-SS) for matched filtering of the received signal [9, 12]. The receiverstructure consists of a matched filter that is matched to the transmitted waveform that representsone symbol, and a tapped delay line that matches the channel impulse response [11]. It is also

possible to implement this structure as a number of correlators that are sampled at the delays

related to specific number of multipath components; each of those correlators can be calledRake finger. A Rake receiver structure is shown in Fig.1.

Figure.1. UWB RAKE receiver structure

The received signal first passes through the receiver filter matched to the transmitted pulse and

is given by

)().(.)(

)(*)()(*)(*)()(

tnTktmhkd

tptntpthtAtr

isk i

i

+

=

+=

+=

(3)

Wherep(-t)represents the receiver matched filter, * stands for convolution operation and

n(t) is the additive white Gaussian noise (AWGN) with zero mean and varianceN0/ 2 . Also,

m (t ) = p (t ) * p ( t ) and n (t ) = n (t ) * p ( t ) .Combining the channel impulse response (CIR) with the transmitter pulse shape and the

matched filter, we have

)(.)(*)(*)()(0

~

i

M

i

i tmhtpthtpth == =

(4)

The output of the receiver filter is sampled at each Rake finger. The minimum Rake finger

separation is Tm = Ts /Nu , whereNuis chosen as the largest integer value that would result inTm spaced uncorrelated noise samples at the Rake fingers

( ) ( )( ) ( )kdtTknhtTnv isk

ls ... 0'

~

0

' ++=++ +

=

(5)

wherelis the delay time corresponding to thelth

Rake finger and is an integer multiple ofTm.

Parametert0

corresponds to a time offset and is used to obtain the best sampling time. Without

loss of generality,t0will be set to zero in the following analysis.

3.2. MMSE STRUCTURE

In reality the noise component due to the physical channel cannot be ignored. In the presence of

additive Gaussian noise at the receiver input, the output of the equalizer at the nth

sampling

instant is given by


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=

=

N

NKknkn

rby (6)

The mean square error (MSE) for the equalizer having 2N+1 taps, denoted byJ(N) is

==

=

2

2)(

N

Nkknknnn

rbxEyxENJ (7)

J(N)with respect to the equalizer coefficients (bk) is obtained by the following differentiation:

0)(

=kdb

NdJ (8)

Equation (7) leads to the necessary condition for the minimum MSE given by

xrr RbR = xrr RRb1

= (9)

WHERE

Txrxrxrxr NRRNRR ))()....0()....(( = (10)

)0()()2(

)1()1()12(

...

...)2().......().......0(

2

++

=

rrNr

rrr

rrr

r

RNRNR

RNRNR

NRNRR

R (11)

3.3. RAKE-MMSE STRUCTURE

The receiver structure is illustrated in Fig. 2 and consists in a Rake receiver followed by a linear

equalizer. As we will see later on, a structure gives better performances over UWB channelswhen the number of equalizer taps is sufficiently large. The received signal first passes through

the receiver filter matched to the transmitted pulse (3). The output of the receiver filter issampled at each Rake finger. The minimum Rake finger separation is Tm= Ts / Nu , whereNu is

chosen as the largest integer value that would result in Tm spaced uncorrelated noise samples atthe Rake fingers(4). In a first approach, complete channel state information (CSI) is assumed to

be available at the receiver. For general selection combining, the Rake fingers (s) are selectedas the largestL (LNu) sampled signal at

Figure.2. UWB RAKE-MMSE receiver structure

the matched filter output within one symbol time period at time instants l ,l = 1, 2, ..., L . In

fact, since a UWB signal has a very wide bandwidth, a Rake receiver combining all the paths ofthe incoming signal is practically unfeasible. This kind of Rake receiver is usually named a

ARake receiver. A feasible implementation of multipath diversity combining can be obtained by


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a selective-Rake (SRake) receiver, which combines theL best, out ofNu, multipath components.Those L best components are determined by a finger selection algorithm. For a maximal ratio

combining (MRC) Rake receiver, the paths with highest signal-to-noise ratios (SNRs) areselected, which is an optimal scheme in the absence of interfering users and intersymbolinterference (ISI). For a minimum mean square error (MMSE) Rake receiver, the

conventional finger selection algorithm is to choose the paths with highest signal-to-

interference-plus-noise ratios (SINRs) [2]. Our case doesnt deal with multiuser UWB

communication but we study channels with high delay dispersion, so the first criterion (Lhighest SNRs) can be chosen. The noiseless received signal sampled at the l

thRake finger in

the nth

data symbol interval is given by equation (5). The Rake combiner output at time t= n.Tsis

( ) ( )'1

'

1

....][ls

L

llls

L

ll

TnnTnvny +++=

==

(12)

Choosing the correct Rake finger placement leads to the reduction of ISI and the performance

can be dramatically improved when using an equalizer to combat the remaining ISI.

Considering the necessary tradeoff between complexity and performance, a sub-optimum

classical criterion for updating the equalizer taps is the MMSE criterion.

4.PERFORMANCEANALYSIS

In this part, due to the lack of place we will only discuss the matrix block computation of linear

equalizers. Furthermore, we suppose perfect channel state information (CSI). Assuming that then data bit is being detected, the MMSE criterion consists in minimizing

)()(

2

ndndE(13)

where d( n ) is the equalizer output. Rewriting the Rake output signal, one candistinguish the desired signal, the undesired ISI and the noise as

( )( )

( )'1

'

~

1

'

~

1

..

)(...)(.)(.)(

ls

L

ll

lsnk

L

lll

L

ll

Tnn

kdTknhndhny

++

++=

=

==

(14)

where the first term is the desired output. The noise samples at different fingers, n (n.Ts + l),

l = 1... L, are uncorrelated and therefore independent, since the samples are taken atapproximately the multiples of the inverse of the matched filter bandwidth. It is assumed that

the channel has a length of (n1 + n2 + 1).Ts. That is, there is pre-cursor ISI from the subsequent

n1 symbols and post-cursor ISI from the previous n2 symbols, and n1 and n2 are chosen large

enough to include the majority of the ISI effect. Using (8), the Rake output can be expressednow in a simple form as

)(][

)()(.)(.)(

~

~

0

0

2

1

nnn

nnkndndny

T

n

k

nkk

+=

++=

=

(15)

where coefficient Ks are obtained by matching (14) and (15).T

21nn)]n-...d(n)....d(n).n[d(nd[n]and +== ]......[

21 0

The superscript denotes the transpose operation. The output of the linear equalizer is obtained as


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( ) ( ) ( )ncncrnycnd TTk

kr

r +== =

2

1

.)( (16)

wherec=[cK1 ...c0 ...cK2]contains the equalizer taps. Also

[ ] [ ] [ ] [ ][ ]TTTT KndndKndn 21 ...... +=

[ ] ( ) ( ) ( )T

KnnnnKnnn

=+= 2~~

1

~

......

(17)

The mean square error (MSE) of the equalizer,

( ) [ ] [ ]

2

ncncndE TT (18)

which is a quadratic function of the vector c, has a unique minimum solution. Here, the

expectation is taken with respect to the data symbols and the noise. Defining matrices R,p and

Nas

[ ] [ ][ ]n.nE T=R (19)

( ) [ ][ ]n.ndE =p (20)

[ ] [ ][ ]n.nE T=N (21)

The equalizer taps are given by

pNRc .)( 1+= (22)and the MMSE is

pNRpJ Td .)(12

min+= (23)

])([22

ndEd =

Evaluating the expectation overR andp with respect to the data and the noise, we have

[ ] [ ]1,1,0 21212

......++++

==KKKKji

T

KK rRp (24)

Where

1nn,1nnk,lji,j,i

T

j,i 2121]f[FandFr ++++==

==

ijkl

ijklf

lk,0

,1

(25)

[ ] [ ][ ]

I..2

Nn.nEN1KK

L

1l

2

l0T

21 ++

=

==

(26)

Where I is the identity matrix. This Rake-equalizer receiver will eliminate ISI as far as the

number of equalizers taps gives the degree of freedom required. In general, the equalizer outputcan be expressed as

( ) ( ) )(.)(.0

10 nwindqndqndi

++= =

(27)


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.with nnn cq = The variance ofw( n ) is

( ) 2.. 0

1

2

1

222

1

NEc p

L

l

K

Ki

inw

=

==

(28)

WhereEpis the pulse energy.Where matrix 0 is the all zero matrix.

The MMSE feedback taps are then obtained in terms of feed forward taps and matrixU.

[c1.ck2]=[c-K1c0]UT

(29)

Conditioned on a particular channel realization, h= [h1hI],an upper bound for theprobability of error using the chernoff bound technique given by

)2

/1exp()(

min

2

min

J

JhddP dnn

(30)

An exact BER expression with independent noise and ISI terms can be expressed as a series

expansion is given by

==

=

2

1

0

1

0

22

)cos(

)sin()2/exp(2

2

1

)

(

N

n

Nnn

z

zoddz

nn zwqz

zwqwz

hddP (31)

Note that ISI comes from the interfering symbols in the range ofN1TsandN2Ts. Parameter z and

w determine the accuracy of the error rate given by (30).we can simply set the qi s that are within the span of the feedback taps to be 0, which

corresponds to zero post-cursor ISI for the span of feedback taps.

5.SIMULATIONSTUDYANDANALYSIS

5.1. Signal Waveform

The pulse shape adopted in the numerical calculations and simulations is the second derivativeof the Gaussian pulse given by

))(t/exp(-2])(t/4-[1=w(t) 22 (32)

The pulse waveform and power spectral density are showed as figure 3.

-1 -0.5 0 0.5 1

x 10-9

-0.5

0

0.5

1

TIME

AMPLITUDE

0 2 4 6

x 1010

0

0.05

0.1

0.15

0.2

FREQUENCY

AMPLITUDE

4 6 8 10 12 14 16

x 109

-120

-100

-80

-60

-40

-20

0

FREQUENCY

PSD

Figure.3. Second derivative of Gaussian pulse


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5.2. Channel Model Parameter (IEEE 802.15.3a)

As we mentioned it before, we study the case of UWB channels CM1, CM2, CM3 and CM4channel models [10]. We have used an oversampling factor of eight for the root raised cosine

(RRC) pulse. According to this sampling rate, time channel spread is chosen equal to 100 for

CM4 and 70 for CM3, this corresponds to respectively 12 =100 / 8 and 9 = 70 / 8 transmittedsymbols. This choice enables to gather 99% of the channel energy. The coherence bandwidths

of CM1, CM2, CM3, and CM4 simulation are 27 MHz, 26 MHz, 10.6 MHz, and 5.9 MHzrespectively. The data rate is chosen to be 200 Mbps, one of the optional data rates proposed forIEEE standard. The size of the transmitted packets is equal to 2560 BPSK symbols including atraining sequence of length 512. CIR remains constant over the time duration of a packet. The

root raised cosine (RRC) pulse with roll off factor =0.5 is employed as the pulse-shapingfilter. The CM1-CM4 indoor channel model is adopted in simulation. The simulated channelimpulse responses for CM1, CM2, CM3 and CM4 are shown in figure 4, figure 6, figure 8

and figure 10.The power delay profiles for CM1, CM2, CM3 and CM4 are plotted in figure

5, 7, 9 and 11 respectively. The simulation parameter settings for the entire four channelmodels are listed in Table.1.

Table.1 Parameter Settings for IEEE UWB Channel Models

Scenario (1/ns) (1/ns) (1/ns) (1/ns) (dB) (dB) g (dB)

CM1 0.0233 2.5 7.1 4.3 3.3941 3.3941 3

CM2 0.04 0.5 5.5 6.7 3.3941 3.3941 3

CM3 0.0067 2.1 14 7.9 3.3941 3.3941 3

CM4 0.0067 2.1 24 12 3.3941 3.3941 3

Figure.4. Channel Impulse Response of CM1 (LOS)

Figure.5. Power Delay Profile of CM1 Channel


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Figure.6. Channel Impulse Response of CM2 (NLOS)





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5.3. BER ANALYSIS

In the case of time domain equalization, we have at first to optimize the number of Rake fingers

and the number of equalizer taps. The Rake fingers are regularly positioned according to time

channel spread and the number of fingers. Figure12, figure 13, figure 14 and figure 15 showsthe effect rake, mmse and rake-mmse using Monte-Carlo simulation. The Rake combiner output

at time t = n.Ts. As expected, using a 5 taps MMSE equalizer to compensate for ISI, a relativeimprovement is observed. The major comparison lies in the rake-mmse receiver having 5 tap,10 rake fingers versus the Rake receiver with 10 rake fingers. Table.2 provides the simulation

parameter.Table.2 Simulation Parameter

Parameter values

Data rate 200 Mbps

Pulse width 0.18

Symbol duration 5ns

Number of equalizer taps 5

Number of Rake fingers 10

Pulse energy 1

Tm 0.1786 ns

Nu 28

Channel spread 100

Pilot carrier 500


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Rake-mmse receiver has around 3dB performance improvement compared to a rake receiver forCM1 channel model as shown in figure 12. Where at 10

-3BER floor, Rake-mmse receiver has

around 1.6dB SNR performance improvement compared to a channel with rake receiver forCM2 channel model as shown in figure 13.

0 2 4 6 8 10 1210

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BER

CM1 CHANNEL

5taps,10 rake fingers-RAKE-MMSE

10 rake fingers-rake

5taps-MMSE

Figure.12. Performance of UWB receivers for CM1 channel model

0 2 4 6 8 10 12 1410

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BER

CM2 CHANNEL



5taps-MMSE



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0 2 4 6 8 10 12 1410

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BER

CM3 CHANNEL



5taps-MMSE


0 2 4 6 8 10 12 14 1610

-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BER

CM4 CHANNEL


5taps-MMSE



Rake-mmse receiver has around1.8dB performance improvement compared to a channel with

rake receivers for CM3 channel model as shown in figure 14. Using CM4 channel data, for

same parameter the simulation results obtained as shown in figure 15.Using Rake-

MMSE, i.e. rake-mmse and a rake receiver a gain of around 4dB is observed. This result

can be explained by considering the fact that at high SNRs it is mainly the ISI that


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affects the system performance whereas at low SNRs the system noise is also a major

contribution in system degradation (more signal energy capture is required). The

performance dramatically improves when the number of Rake fingers and the equalizer

taps are increased simultaneously in Rake-MMSE receiver. As expected the receiver has

better performance over CM3 with smaller delay spread than CM4 on non-line of sight

(NLOS) indoor channel models.

6.CONCLUSION

The receivers combats inter-symbol interference by taking advantage of the Rake and

equalizer structure by using different UWB channel models CM1-CM4 for high data

rate WPAN system. For a MMSE equalizer operating at low to medium SNRs, the

number of Rake fingers is the dominant factor to improve system performance, while, at

high SNRs the number of equalizer taps plays a more significant role in reducing error

rates. The IEEE 802.15a (TG3a) standard which is to provide a low complexity, low

cost, low power consumption and high data-rate among Wireless Personal Area

Network (WPAN) devices. One can observe at BER floor having high SNR values thereceiver has better performance over CM1 (LOS) with smaller delay spread than CM2

(NLOS) channel models. Rake-mmse receiver has around1.8dB performance

improvement in CM3 (NLOS) channel model compared to CM4 (NLOS) channel

model. This architecture has opened up new directions in designing efficient adaptive

equalizers and can be implemented in DSP processors for real - time applications.

REFERENCES

[1] A. Rajeswaran, V.S. Somayazulu and J. Foerster, "Rake performance for a pulse based UWB

system in a realistic UWB indoor channel",IEEE ICC03., vol. 4, pp. 2879-2883, May 2003.

[2] S. Gezici, H. V. Poor and H. Kobayashi, "Optimal and Suboptimal Finger Selection Algorithms

for MMSE Rake Receivers in Impulse Radio Ultra-Wideband Systems", in Proc IEEE WCNC2005, New-Orleans, Mar. 2005.

[3] J. R. Foerster, "The effect of multipath interference on the performance of UWB systems in an

indoor wireless channel", in Proc. 2001 Spring Vehicular Technology Conf., pp. 1176-1180, May

2001.

[4] J. D. Choi and W. E. Stark, "Performance of ultra-wideband communications with suboptimal

receivers in multipath channels",IEEE J. Select. Areas Communication, vol. 20, pp. 1754-1766,

Dec. 2002.

[5] D. Cassioli, M. Z. Win, F. vAtalaro and F. Molisch, Performance of low-complexity RAKE

reception in a Realistic UWB channel, in Proc. Int. Conf. Communication (ICC), vol. 2, May

2002, pp. 763-767.

[6] T. Strohmer, M. Emani, J. Hansen, G. Papanicolaou and A. J. Paulraj, "Application of Time-

Reversal with MMSE Equalizer to UWB Communications", in Proc. IEEE Globecom04., vol.5, pp. 3123-3127, Dec. 2004.

[7] B. Mielczarek, M. O. Wessman and A. Svensson, Performance of Coherent UWB Rake

Receivers With Channel Estimators, in Proc. Vehicular Technology Conf. (VTC), vol .3, Oct.

2003, pp. 1880-1884.

[8] A. Rajeswaran, V. S. Somayazulu and J. R. Forester, Rake Performance for a Pulse Based UWB

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[9] Y. Ishyama and T. Ohtsuki, Performance Evaluation of UWB- IR and DS-UWB with MMSE-

frequency Domain Equalization (FDE), in Proc. IEEE Global Telecommunication Conf.

(Globecom), vol. 5, Nov-dec 2004, pp. 3093-3097.

[10] J.F. Foerster, M. Pendergrass and A. F. Molisch, "A Channel Model for Ultrawideband Indoor

Communication", MERL (Mitsubishi Electric Research Laboratory) Report TR-2003-73, Nov.

2003.

[11] P. Balaban and J. Salz, Optimum diversity combining and equalization in digital data

transmission with applications to cellular mobile radio-part I: theoretical considerations, IEEE

Trans. Communication, vol. 40, pp. 885-894, May 1992.

[12] M.Z. Win, R.A Scholtz, Ultra-wide bandwidth time- hopping spread spectrum impulse radio

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Authors

Dr.Susmita Das, Ph.D, is Associate Professor of Electrical Engineering,

NIT, and Rourkela, India. She has twenty years of teaching and research

experience and has many research papers to her credit. She is Member IEEE,Fellow IETE, LM ISTE and Member IEI. Her research interests include

Wireless Communication, DSP, and Application of Soft Computing

Techniques etc.

Bikramaditya Das received his B.Tech in Electronics and

Telecommunications Engineering from the University of B.P.U.T, Rourkela,

Orissa, India, in 2007. From 2008 to till now he is a research Fellow under

the Department of Electrical Engineering at the N.I.T, Rourkela, India. He is

a Member IEI.

a comparision study of time domain equalization technique using ultrawide band receivers performance...

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